a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
C(b(x1)) → B(c(c(x1)))
C(b(x1)) → A(b(c(c(x1))))
B(c(x1)) → A(x1)
C(b(x1)) → C(c(x1))
C(b(x1)) → C(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C(b(x1)) → B(c(c(x1)))
C(b(x1)) → A(b(c(c(x1))))
B(c(x1)) → A(x1)
C(b(x1)) → C(c(x1))
C(b(x1)) → C(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B(c(x1)) → A(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 1/8.
POL(c(x1)) = 1/2 + (2)x_1
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = (2)x_1
POL(A(x1)) = (1/2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
C(b(x1)) → C(c(x1))
C(b(x1)) → C(x1)
a(a(x1)) → b(x1)
b(c(x1)) → a(x1)
c(b(x1)) → a(b(c(c(x1))))